Method of processing production well logging data

ABSTRACT

In accordance with an illustrative embodiment of the present invention, a method is disclosed for processing production logging data in order to determine, in a two-phase, water-oil, flow, the flowrate of one of the phases at different depths of a production well. At each depth, data representative of the total flowrate and of the proportion of total cross section of pipe occupied by one of the phases, designated &#39;&#39;&#39;&#39;hold up,&#39;&#39;&#39;&#39; is generated. For each depth, the slippage velocity between the two phases is computed from the data representative of hold up and of a parameter which is a function of the difference in density between the two phases. The flowrate of each phase is then computed from the previously computed values of slippage velocity and from the data representative of total flowrate and hold-up. This method gives precise quantitative data making it possible to determine the operations required to improve the production of the well.

sea- +22 W a 3,909,693: s; y ,5}

United Stat 4 er i Nicolas j g 1 1451 Sept. 30, 1975 l l METHOD OFPROCESSING PRODUCTION N0. SPE-l908, Society of Petroleum Engineers ofWELL LOGGING DATA AIME, i967.

[75] Inventor: Yves Nicolas, Versailles, France Prunary Lxammer-R.Stephen Dildme, Jr.

[ l Assigncci Schlumberger Technology Attorney, Agent, or FirmCooper,Dunham, Clark,

Corporation, New York, NY. G iffi & Mel-1m [22] Filed: Aug. 11, 1971[57] ABSTRACT 1211 Appl. No.: 170,806

In accordance with an illustrative embodiment of the present invention,a method is disclosed for processing [30] Forelgn Apphcatlon Pnonty Dataproduction logging data in order to determine, in a Aug. 12, 1970 France70.29635 tw0 pha e, water-oil, flow, the flowrate of one of the phasesat different depths of a production well. At

[52] US. Cl 35/l 235/92 each depth, data representative of the totalflowrate 1 and of the proportion of total cross section of pipe oc- Int.Cl. upied one. of the phases designated hold up is l l Field Of Search73/194 generated. For each depth, the slippage velocity be- 3 235/92 FL,tween the two phases is computed from the data representative of hold upand of a parameter which is a i 1 References cued function of thedifference in density between the two UNITED STATES PATENTS phases. Theflowrate of each phase is then computed 3304766 2/1967 Hubbyw 73mm fromthe previously computed values of slippage ve- 3 3g5 g 5 19 3 ROSS, 73locity and from the data representative of total flow- $488,996 1/1970Pfrchm 73/61 1 rate and hold-up. This method gives precise quantita-3,545,270 12/1970 Chang 73/194 tive data making it possible to determinethe opera- OTHER PUBLICATIONS tions required to improve the productionof the well.

Curtis, M. R Flow Analysis in Producing Wells, Paper Claims, 8 DrawingFigures +D.c. +orc.

r; A E COMPUTE CIRCUIT COM PUTERI Y (1Y VSA MULTIPLY CIRCUIT DIFF. CKT,

R I l U.S. Patent Sept. 30,1975 Sheet 1 of 5 3,909,603

FIG.2

22 :2: 5;; /X 2 42, z 22/ /y 7/2 INVENTOR. Yves Nicolas US. Patent Sept.30,1975 Sheet 2 of5 3,909,603

.7 WATER HOLDUP Yw US. Patent Sept. 30,1975 Sheet 3 of5 3,909,603

V (FT/Ml N) Vw(FT/MIN) 590 BARRELS DAY US. Patent Sept. 30,19753,909,603

Sheet 5 of 5 FIG.7

ISET INTERVAL COUNTER =1 ITSZ READ CONSTANT PARAMETERS AI,I ,M ,AD,O' 8.MEASURED PARAMETERS Yw & Q FOR INT- ERVAL TO BE CONSIDERED & STORE INMEMORY I COMPUTE A? WITH EQ. (s)

SET D LOWER DEPTH LEVEL L READ MEASURED PARAMETERS fw 8. QT AT DEPTHLEVEL D COMPUTE v5 USING EQ.(7)

i COMPUTE Qw & Q WITH EQS.,(5) & (6) & VALUE OF Vs COMPUTED INPRECEEDING STEP INCREMENT D BY AD 81 I INCREMENT I INTERVAL INTERVAL TOBE COUNTER I CONSIDERED BY ONE I I I METHOD OF PROCESSING PRODUCTIONWELL LOGGING DATA This invention relates to a method for the processingof production logging data and more particularly to a method makingitpossible to determine the flowrate of each phase of a multiple-phaseflow in 'a production well.

After a wellbore is drilled in the earth, and sufficient quantities ofeasily removable oil and/or gas are found,

the well is cased and cemented, and perforated at desired depths toproduce (bring to the surface) the oil and/or gas. Production loggingconcerns the measurement of parameters useful in evaluating the wellafter completion, and particularly, for evaluating the nature andmovement of fluids within the well.

The fluid flowing in a production well is generally a most wells areperforated at a number of depth levels thus causing fluid to enter thewell at a number of levels. Hold up" is the proportion of the totalcross section of a well occupied by a givenphase. Thus, there can bewater hold-up, oil hold-up and gas hold-up.

There are numerous apparatus available for measuring this information.To measure the total flowrate, spinner flowmeters are generally used, inparticular as described in copending applications Ser. No. 867,994 filedby Fierfort on Oct. 21, 1969, and now abandoned, and Ser. No. 872,97lflledby Bonnet on Oct. 31, 1969, now Pat. No. 3,630,078. To obtain thehold-up of each phase, one may for example measure the average densityof the flowing fluid either by means of a differential pressureapparatus, called a gradiomanometer, of the type described in the USPat. No. 3,455,157 issued to Lahye etal. on July 15, 1969, or by meansof a vibrating densimeter, in particular as described in the US. Pat.No. 3,225,588. It is also possible to obtain the composition of theflowing fluid by means of nuclear apparatus of the gamma ray emissiontype, or in certain cases by average capacitance measurements. Anotherknown method is to' combine two of the above sensors so as to obtainwith a single apparatus the total flowrate and the hold-up of eachphase.

It may be thought that, from these two quantities, it is simple todetermine the relative flowrate of each phase. In fact, in a verticalrising flow, the phases have different velocities, the lighter phaseflowing faster than the heavier phase. Consequently, the cut of thephase (i.e. the flowrate of each phase divided by the total flowrate)is'different from the measured hold-up. In order to determine theflowrate of each phase, it is necessary to know another quantity,.forexample the slippage velocity, i.e. the difference in. velocity betweenthe two phases. It has hitherto been assumed that this slippage velocityis constant along the entire length of the well, and only a function ofthe density difference between the two phases; When making thisassumption for high flowrates, it is possible to obtain reasonablyaccurate results due to the fact that the slippage velocity remains lowin relation to total flow-rate for such high flow rates. On the otherhand, in the case of low flow rates, the above assumption leads toerroneous results.

It is therefore an object of the present invention to determine withreasonable accuracy the slippage velocity'and/or'the flowrate ofindividual phases in a multi-- ple phasic flow for both high and lowflowrates.

A further object of the invention is to provide an accuraterepresentation of the nature and of the composition of the fluidproduced at different levels of a well.

In accordance with one aspect of the present invention, a method ofprocessing well logging data comprises deriving a measurementrepresentative of the proportion of one phase of a multiple phase flowin a well -at-a selected depth leveland using this derived measurementin conjunction with a predetermined value of the apparent difference indensity between the. two phases of the-multiple phase flow to produce arepresentation of the difference in velocity between two phases of themultiple phase flow at the selected depth level. I

In accordance with the another aspect of the present invention, a methodof processing well logging data comprises deriving a measurementrepresentative of the proportion of one phase of a multiple phase flowin a well at a selected .depth level and deriving a measure mentrepresentative of the total rate of flow of the fluid in the well at theselected depth level. These derived measurements are combined to producea representation of the flow rate of at least one phase of the multiplephase flow at the selected depth level. One of the constants used inproducing the representation of flow rate is a predetermined valueforthe apparent density differencebetween the above mentioned twophases. This predetermined value can vary fromone well to another, orperhaps even between horizons of one well.

The characteristics and advantages of the invention will be betterunderstood through the description to follow given by way ofnon-limitative examples with reference to the accompanying drawings inwhich:

FIG. I is a simplified diagram of a diphasic flow in a producing well;

FIG. 2 is a plot of the slippage velocity versus the density differencebetween the two phases of aflo wing fluid for different values of waterhold-up;

FIG. 3 is a-plot of slippage velocity versus their density differencefor different .values of water hold-up;

FIG. .4 is a chart giving a graphical solution of the method of theinvention; f

-FIG. 5 is the diagram of circuits for the processing. of data inaccordance with .themethod of theinvention;

FIG. 5A is a block diagram ofa circuit of the FIG. 5;

FIG. 6 is a form of presentation of the results obtained by the methodof the present invention; and

FIG. 7 is a flow diagram representation of a computer program forprocessing production logging data in accordance with the presentinvention.

,For a proper understanding of the invention, we shall first establishtheequations relate relatte the different parameters of a diphasic flow.In this connection, referring to FIG. 1, a schematic representation isgiven of a section of a casing 10 of aproducing well. In this casingflows a diphasic fluid produced byunderground formations and including aheavy phase 11, for example water, and a light phase l2, for exampleoil. To permit the equations to be formulated, two separate phases arerepresented, flowing parallel to each other. In reality, the two phasesare mixed, one of these phases generally being in the form of bubbles insuspension in the other phase which is called the continuous phase. If Yis the water hold-up, i.e. the ratio between the volume of water inplace and the total volume of the fluid, it can be seen that the waterflow-rate Q and the oil flowrate Q, are given by the equations:

0,. Y A v,

in which A is the internal area of the cross-section of the casing and Vand V,, are respective flowrates of the water phase and the oil phase.

Moreover, the total flowrate Q, is given by the equation:

If the quantitites of Q, and Y can be obtained through measurements inthe well, there are three equations with four unknowns, namely Q Q V andV To solve this system of equations, a fourth equation is needed, forexample:

in which V, is the slippage velocity between the two phases. If thisslippage velocity can be determined, we can in fact solve the system ofequations 1 to 4 to obtain Q and Q as follows:

As discussed earlier, it has in the past been assumed that the slippagevelocity is constant along the length of the well and only a function ofthe density difference between the two phases. Thus, in the past, thedensity difference would be first determined from density measurementsto enable a determination of a value of slippage velocity for the well.To determine this one shot value of slippage velocity for bubble flow,the following equation can be used for bubbles of diameter 0.1 cm to 2cm:

Ill

where K is constant, (T is the interfacial tension on the bubblesurface, Ap is the density difference between the bubble phase andcontaining fluid, p,,-,, is the density of the containing fluid, g isthe acceleration of gravity. For more information on this expression,see the article entitled Average Volumetric Concentration in Two- PhaseFlow Systems in Vol. 87 of the Journal of Heat Transfer by Zuber andFindley.

After finding the value of V equations 5 and 6 could be solved for Q andQ,,.. However, after a great deal of research, it has been found thatthis assumption of one value of slippage velocity is not always correct.Recent laboratory research has shown that the slippage velocity V, is afunction of both the water hold-up Y and of certain physical propertiesof the phases such as their density, their viscosity, and the surfacetension of the bubbles. More specifically, this research has found thatthe slippage velocity V, is given by the following where y l AP 35 :1+0.03 Log (8) where P Pu P" where p,,. is the density of water and ,0 isthe density of oil.

As it is practically impossible to obtain the value of the surfacetension, two possibilities exist for determining the parameter Ap. Onecan measure the density difference Ap in accordance with equation 9 atthe surface and correct this measured value to take into account thetemperature and pressure conditions at the considered depth. Thiscorrected value can be used as the value of the parameter Ap with theunderstanding that average values for the interfacial tension 0' and theoil viscosity 11. are being used. The other possibility is to determinethe value of the parameter Ap from surface measurements of the totalflowrate Q, and water flowrate Q,,., and also from a measurement of Y,,.made immediately above the production zone closest to the surface, thismeasurement Y corresponding to the surface flow. From these values, Q,,Q and Y one can determine the slippage velocity by using equation 5. Bymeans of equation 7, knowing Y and V one can obtain the value of theparameter Ap' applicable over the entire length of the well. This value,which includes the i parameter Ap (equation 8), takes into account thesurface tension and the viscosity and probably will not be equal to theactual density difference Ap between the phases.

FIG. 2 shows equations 7 to 9 in graphical form. In FIG. 2, a set ofcurves 13 to 21 has been plotted, each of which represents, for a givenwater hold-up, the slippage velocity V, as a function of the parameterAp' given in equation 8.

From FIG. 2, it is possible to make two observations. It can first ofall be seen that the slippage velocity increases when the densitydifference increases. Moreover, it is seen that this slippage velocityincreases when the water hold-up Y increases. It was hitherto consideredthat the slippage velocity was constant along the entire length of aproducing well, even when the water hold-up varied. The curves of FIG. 2show thatthis prior method of interpretation gives erroneous results,especially for low flowrates in which the slippage velocity isrelatively high compared with the average flowrate of the fluid.

' It would perhaps be more useful to represent equation 7 by a plot ofslippage velocity V vs water hold-up Y for different values of Ap sincea value of Ap is selected before computing slippage velocity V withmeasured values of water hold-up Y,,.. Using the curves of FIG. 3 andhaving a predetermined value of Ap it is possible, in accordance withthe present invention, to determine the slippage velocity V, with valuesof water hold-up Y measured by a densimeter or a gradiomanometer. Oncethis magnitude V has been obtained, it will be easy to determine theflowrates Q,,. and Q,, by means of equations 5 and 6.

Just as it is possible, from the curves'of FIG. 3, to find the equationwhich relates the slippage velocity to the apparent density differenceand to the water hold-up, one can also solve equations 5 and 6graphically. In order for this graphical solution to be applicable toall well casings of any internal area A, a parameter V, called thesuperficial velocity, and defined as the flow per unit area is used.This superficial velocity is then independent of the dimensions of thecasing, and we have:

t Qw/A V, Q /A where the subscripts t, w and have the same meaning asbefore. Combining equations 10, l 1 and 12 with equations and 6, thesuperficial velocities of the water and oil are then given by theequations:

FIG. 4 represents an alignment chart permitting the graphical solutionof the equations 13 and 14. This figure represents, from left to right,three axes, 23, 24 and 25, on which are located respectively the valuesV,, V and V A family of curves 26, corresponding to the different valuesof Ap', is intersected by vertical lines 27 corresponding to thedifferent values of the Water holdup Y,,.. To each value of Ap therethus corresponds a curve of the family 26 and to each value of Y a pointon this curve. If the total superficial velocity V, is known, we needonlyjoin this value, located on the axis 23 on the left, to thepreviously defined point of the curve of the family 26. This lineintersects the axes 24 and 25 at two points which give respectively thesought values of V and V Conversely, by means of the alignment chart ofFIG. 4, it is possible to determine the value of the parameter Apapplicable over the entire length of the well if one knows the valuesofV V and Y corresponding to the same flow. As the values V, and V canbe easily determined for the flow at the surface of the well, one needonly carry out a measurement of Y l in the part of the casing locatedimmediately over the perforations closest to the surface. The linejoining the values V, and V measured on the surface will intersect thevertical line of the abscissa Y at a point defining a curve of thefamily 29 which corresponds to the sought value of Ap.

From the foregoing, it can be seen that it is possible to determine atdifferent depths the flowrate of the water and oil flowing in the wellwith oil bubbles in suspension in a continuous water phase. In simplecases, these values may be determined manually, either by calculation,or graphically, as indicated above. On the other hand, for more complexcases, it will be necessary to use automatic computation methods. Themethod of the invention may be perfectly adapted to automaticcalculations performed by a computer for example. In fact, as all of therelationships between the different parameters are known, calculationsmay be carried out by means of electronic circuits adapted toautomatically process signals representative of the total flowrate Q,and of the water hold-up Y FIG. 5 shows such circuits. In FIG. 5, a welltool 33 is supported in a cased well 34 by a cable 35. The well 34 isperforated at a plurality of points 36 such that formation fluid willenter the well at these points. The well tool 33 includes a spinnerflowmeter and gradiomanometer to measure the total flowrate Q andmixture density p of the fluid. From p the water hold-up Y, can bederived from the following expression:

where (p,,),;,, and' (p,,.),, are predetermined values of bottom holeoil density and water density respectively.

The signals'from the well tool 33 are applied to signal processingcircuits 38 which perform a number of standard operations, such asimpedance-matching, calibration correction, etc. The gradiomanometersignal p,,,, is applied to a computing circuit 39 which computes thevalue of water hold-up Y,,.. To accomplish this, a signal proportionalto(p,,) derived from a potentiometer 41 is subtracted from the p,,,signal by a difference circuit 40 and the resulting signal multiplied bythe constant through the action of a potentiometer 42 to produce Y ThisY signal as well as the total flowrate signal Q are applied to acomputer circuit 45 to compute Q,,- and Q,,. To accomplish this, thesignals proportional to Y and Q are applied to a computer circuit 46 towhich is also applied signals representative of the predeterminedconstants Ap' and p,,.. The circuit 46 delivers an output signalproportional to V computed in accordance with equation 7. The signalY,,. is also applied to a calculation circuit 47 adapted to deliver anoutput signal proportional to Y .(l Y,, The circuits 46 and 47 areconnected to the inputs of another calculation circuit 48 to which isapplied the value of the area A so as to generate a signalrepresentative of Y l Y V ,A. The signal Y and a signal representativeof Q, are also applied to a multiplication of circuit 49 whoseoutputsignal is proportional to Y,, Q,. The outputs of the circuits 48 and 49are connected to the input of a subtraction circuit 50 which gives thedifference of these two input signals; that is, Q,,. Y Q, Y,, IY,,.)V,A. The signal Q,,. and the signal Q, are applied to a recorder 51 whosemovement is proportional to depth by virtue of a wheel 52 coupled to thecable 35 to rotate therewith and driving a mechanical linkage 53 coupledto the film drive of the recorder 51.

FIG. A shows how the V, computer 46 might be constructed. The measuredquantity Y and the predetermined constants Ap' and p are applied to acomputation circuit 55 which computes The fourth root of this quantityis taken by a circuit 56, multiplied by 22.5 in a circuit 57. A circuit58 computes 24 (lY,,.) and a circuit 59 takes the third root of thisquantity. A difference circuit 60 is responsive to the output signalsfrom circuits 57 and 59 to produce a signal proportional to V FIG. 6represents a recording which may be given by the recorder 51. On theleft partis a schematic representation of the production well consistingof a casing 61, perforated opposite two production zones 62 and 63. Onthe upper part of the casing 61 is fixed the lower end of a productionstring 64. To the right of this schematic representation there is a zonewhose ordinate is graduated in depths and whose abscissa in flowrateunits (Barrels/day, for example). In this zone a first curve 65 is shownrepresenting the total flowrate Q given for example by a spinnerflowmeter. A second curve 66 represents the water flowrate O calculatedin accordance with the method of the invention from the measurements ofthe flowmeter and a gradiomanometer for example. The zone locatedbetween the curves 65 and 66 thus represents the oil production of thewell. By means of such curves, one immediately sees the nature and thecomposition of the fluid produced by each zone. Thus, for example, thezone 63 is composed of a lower part which produces only water, a middlepart which does not produce any fluid and an upper part which producesboth water and oil in the proportions of water and 80% oil. These curvesthus give precise quantitative information which is directly utilizableand which in particular makes it possible to determine the operations tobe performed to improve the production and the efficiency of the well.

Now turning to FIG. 7, there is shown a flow diagram representation of acomputer program for practicing the method of the present invention.After the program start, the numerical values in feet of the upper andlower depth levels U and L respectively of the interval for which datais to be processed are read and stored in memory as represented by block70. Next, the constant parameters Ap, pw. t... 0" and AD and themeasured parameters Y and Q are read interval L to U, as represented byblock 71. (AD is the interval between depth levels to be considered).Then, Ap' is computed from equation 8 and D, the depth level presentlyunder consideration, is set equal to L. (See blocks 72 and 73.) Next,the measured quantities Y and Q at the presently considered depth levelD are read from memory and V, is computed in accordance with equation 7.(See blocks 74 and 75.) Then, Q and Q are computed using the value of Vcomputed in step 75 as well as the measured values of Y and Q at depthlevel D and all desired computations are outputted. (See elements 76 and77.)

As represented by a decision element 78, it is determined if the lastdepth level of the interval to be considered has been reached and ifnot, D is incremented by AD (see element 79) and the program recycles tostep 74 to consider the next depth level. If D is U, the program can, ifdesired, have facility to determine if another interval is to beconsidered. Otherwise, the program stops at this point, as representedby the dashed line connection between element 78 and element 80. If theprogram is to be able to consider other depth levels, an intervalcounter is needed. (See elements 81 and Each of the steps of thedetailed flow diagram of FIG. 7 is directly translatable to any one of anumber of standard computer languages, such as Pl /1, and can beperformed on a conventional general purpose computer of a suitable sizeand a suitable configuration, such as an IBM 360/65 of conventionalconfiguration.

While there have been described what are at present considered to bepreferred embodiments of this invention, it will be obvious to thoseskilled in the art that various changes and modifications may be madetherein without departing from the invention, and it is, therefore,intended to cover all such changes and modifications as fall within thetrue spirit and scope of the invention.

What is claimed is:

l. A method of machine processing well logging data, comprising:

deriving a measurement representative of the proportion of one phase ofa multiple phase flow in a well at a selected depth level;

deriving a measurement representative of the total rate of flow of thefluid in a well at said selected. depth level; and combining with amachine said derived measurements with a predetermined value of theapparent difference in density between two phases of said multiple phaseflow to produce a representation of the flow rate of at least one phaseof said multiple phase flow at said selected depth level in a well. 2.The method of claim 1 wherein the step of combining includes combiningsaid phase proportion measurement with said predetermined densitydifference value to compute a representation of the difference invelocity between said two phases, and combining said representation ofvelocity difference with said derived measurements to produce said flowrate representation.

3. A method of machine processing well logging data to determine in atwo phase, water, oil flow through a conduit, the flow rate of at leastone phase wherein a value of the apparent difference in density betweensaid water and oil is predetermined before processing data, comprising:

deriving a measurement representative of the proportion of one phase ofsaid two phase flow in a well at a selected depth level;

deriving a measurement representative of the total rate of flow of thefluid in a well at said selected depth level; and

combining with a machine said derived measurements with saidpredetermined density difference value to produce a representation ofthe flow rate 9 of at least one phase of said two phase flow at saidselected depth level in a well.

4. The method of claim-3 wherein the step of combining includescombining said phase proportion measurement with said predetermineddensity difference value to compute a representation of the differencein-velocity between said two phases, and combining said representationof velocity difference with said derived measurements to produce saidflowrate representation.

5. The method of claim 4 wherein said phase proportion measurement isthe proportion of water in said two phase flow.

6. The method of claim 5 wherein said water proportion measurement Y iscombined with said value of density difference Ap to produce saidvelocity difference representation V in accordance with the express1on:

where X and Z are constants and p is a predetermined value of thedensity of water.

7. The method of claim 6 wherein said representation V is combined withsaid flowrate measurement Q and said water phase proportion measurementY to produce a representation of the flowrate Q,,. of said water phasein accordance with the expression:

where A is the internal area of the cross section of conduit throughwhich said water oil passes, whereby the flowrate of said oil phase isrepresented by the difference between the measured total flowrate Q andthe produced flowrate Q,,..

8. A method of machine processing well logging data, comprising:

deriving a measurement representative of the proportion of one phase ofa multiple phase flow in a well at a selected depth level;

combining in a machine said derived measurement in conjunction with apredetermined value of the apparent difference in density between twophases of said flow to produce a representation of the difference invelocity between said two phases of said multiple phase flow at saidselected depth level in a well.

9. The method of claim 8 wherein said two phases are water and oil andsaid phase proportion measurement is the proportion of water in said twophase flow.

10. The method of claim 9 wherein said water proportion measurement Y iscombined with said value of apparent density difference Ap to producesaid velocity difference representation V in accordance with theexpression:

where X and Z are constants and p is a predetermined value of thedensity of water.

11. Apparatus for processing well logging data, comprising:

means for deriving'a measurement representative of the proportion of onephase of a multiple phase flow in a well at a selected depth level;means for deriving a measurement representative of the total rate offlow of the fluid in'a well at said selected depth level; and i i meansfor combining said derived measurements with a predetermined value ofthe apparent difference in density between two phases of said multiplephase flow to produce a represen tation of the flow rate of atleast onephase of said multiple phase flow at said selected depth levelin a well.

12. Apparatus as in claim 11 wherein the combining means include meansfor combining said phase proportion measurementwith said predetermineddensity difference value to compute a representation of the differencein velocity between said two phases, and means for combing saidrepresentation of velocity difference with said derived measurements toproduce said flow rate representation.

13. Apparatus for processing well logging data to determine in a twophase, viater, oil flow through a conduit, the flow rate of at least onephase wherein a value of the apparent difference in density between saidwater and oil is predetermined before processing data, comprising:

means for deriving a measurement representative of the proportion of onephase of said two phase flow in a well at a selected depth level;

means for deriving a measurement representative of the total rate offlow of the fluid in a well at said selected depth level; and

means for combining said derived measurements with said predetermineddensity difference value to produce a representation of the flow rate ofat least one phase of said two phase flow at said selected depth levelin a well.

14. Apparatus as in claim 13 wherein the combining means include meansfor combining said phase proportion measurement with said predetermineddensity difference value to compute a representation of the differencein velocity between said two phases, and means for combining saidrepresentation of velocity difference with said derived measurements toproduce said flowrate representation.

15. Apparatus as in claim 14 wherein said phase proportion measurementis the proportion of water in said two phase flow.

16. Apparatus as in claim 15 wherein said water proportion measurement Yis combined with said value of density difference Ap' to produce saidvelocity difference representation V in accordance with the expression:

where X and Z are constants and p is a predetermined value of thedensity of water.

17. Apparatus as in claim 16 wherein said representation V, is combinedwith said flowrate measurement Q and said water phase proportionmeasurement Y v to produce a representation of the flowrate Q of Ehidwater phase in accordance with the expression:

where A is the internal area of the cross section of conduit throughwhich said water-oil flow passes, whereby the flowrate of said oil phaseis represented by the difference between the measured total flowrate Qand the produced flowrate Q 18. Apparatus for processing well loggingdata, comprising:

means for deriving a measurement representative of the proportion of onephase of a multiple phase flow in a well at a selected depth level; andmeans for utilizing said derived measurement in conjunction with apredetermined value of the apparent difference in density between twophases of said flow to produce a representation of the difference invelocity between said two phases of said with the expression:

Q lz( l-Y,,.)

where X and Z are constants and p is a predetermined value of thedensity of water.

UNITED STATES PATENT AND TRADEMARK OFFICE QETIFICATE OF CURRECTIONPATENT NO. 3,909,603

DATED September 30, 1975 INVENTOR(S) 3 Yves Nicol-as it is certifiedthat error appears in the above-identified patent and that said LettersPatent are hereby corrected as shown below:

Col. 2, line 62, "relatte", should read relate Col. 5, line 20,"parameter V, should read parameter T7 Col. 9, line 33, equation [Q (l-Y)Q +Y (l-Y )A V W W should bedeleted.

Col. 12 line 7, "is" after the word "measurement" should be deleted.

Signed and Sealed this thirteenth Day of April1976 [SEAL] Arrest:

RUTH C. MASON C. MARSHALL DANN Arresting Ofjicer ('mnmissimu'ruj'latvrirs and Trademarks

1. A method of machine processing well logging data, comprising:deriving a measurement representative of the proportion of one phase ofa multiple phase flow in a well at a selected depth level; deriving ameasurement representative of the total rate of flow of the fluid in awell at said selected depth level; and combining with a machine saidderived measurements with a predetermined value of the apparentdifference in density between two phases of said multiple phase flow toproduce a representation of the flow rate of at leasT one phase of saidmultiple phase flow at said selected depth level in a well.
 2. Themethod of claim 1 wherein the step of combining includes combining saidphase proportion measurement with said predetermined density differencevalue to compute a representation of the difference in velocity betweensaid two phases, and combining said representation of velocitydifference with said derived measurements to produce said flow raterepresentation.
 3. A method of machine processing well logging data todetermine in a two phase, water, oil flow through a conduit, the flowrate of at least one phase wherein a value of the apparent difference indensity between said water and oil is predetermined before processingdata, comprising: deriving a measurement representative of theproportion of one phase of said two phase flow in a well at a selecteddepth level; deriving a measurement representative of the total rate offlow of the fluid in a well at said selected depth level; and combiningwith a machine said derived measurements with said predetermined densitydifference value to produce a representation of the flow rate of atleast one phase of said two phase flow at said selected depth level in awell.
 4. The method of claim 3 wherein the step of combining includescombining said phase proportion measurement with said predetermineddensity difference value to compute a representation of the differencein velocity between said two phases, and combining said representationof velocity difference with said derived measurements to produce saidflowrate representation.
 5. The method of claim 4 wherein said phaseproportion measurement is the proportion of water in said two phaseflow.
 6. The method of claim 5 wherein said water proportion measurementYw is combined with said value of density difference Delta Rho '' toproduce said velocity difference representation Vs in accordance withthe expression:
 7. The method of claim 6 wherein said representation Vsis combined with said flowrate measurement QT and said water phaseproportion measurement Yw to produce a representation of the flowrate Qwof said water phase in accordance with the expression: Qw YwQT -Yw(1-Yw)A Vs (Qo (1-Yw)QT + Yw(1-Yw)A Vs ) where A is the internal areaof the cross section of conduit through which said water oil passes,whereby the flowrate of said oil phase is represented by the differencebetween the measured total flowrate QT and the produced flowrate Qw. 8.A method of machine processing well logging data, comprising: deriving ameasurement representative of the proportion of one phase of a multiplephase flow in a well at a selected depth level; combining in a machinesaid derived measurement in conjunction with a predetermined value ofthe apparent difference in density between two phases of said flow toproduce a representation of the difference in velocity between said twophases of said multiple phase flow at said selected depth level in awell.
 9. The method of claim 8 wherein said two phases are water and oiland said phase proportion measurement is the proportion of water in saidtwo phase flow.
 10. The method of claim 9 wherein said water proportionmeasurement Yw is combined with said value of apparent densitydifference Delta Rho '' to produce said velocity differencerepresentation Vs in accordance with the expression:
 11. Apparatus forprocessing well logging data, comprising: means for deriving ameasurement representative of the proportion of one phase of a multiplephase flow in a well at a selected depth level; means for deriving ameasurement representative of the total rate of flow of the fluid in awell at said selected depth level; and means for combining said derivedmeasurements with a predetermined value of the apparent difference indensity between two phases of said multiple phase flow to produce arepresentation of the flow rate of at least one phase of said multiplephase flow at said selected depth level in a well.
 12. Apparatus as inclaim 11 wherein the combining means include means for combining saidphase proportion measurement with said predetermined density differencevalue to compute a representation of the difference in velocity betweensaid two phases, and means for combing said representation of velocitydifference with said derived measurements to produce said flow raterepresentation.
 13. Apparatus for processing well logging data todetermine in a two phase, water, oil flow through a conduit, the flowrate of at least one phase wherein a value of the apparent difference indensity between said water and oil is predetermined before processingdata, comprising: means for deriving a measurement representative of theproportion of one phase of said two phase flow in a well at a selecteddepth level; means for deriving a measurement representative of thetotal rate of flow of the fluid in a well at said selected depth level;and means for combining said derived measurements with saidpredetermined density difference value to produce a representation ofthe flow rate of at least one phase of said two phase flow at saidselected depth level in a well.
 14. Apparatus as in claim 13 wherein thecombining means include means for combining said phase proportionmeasurement with said predetermined density difference value to computea representation of the difference in velocity between said two phases,and means for combining said representation of velocity difference withsaid derived measurements to produce said flowrate representation. 15.Apparatus as in claim 14 wherein said phase proportion measurement isthe proportion of water in said two phase flow.
 16. Apparatus as inclaim 15 wherein said water proportion measurement Yw is combined withsaid value of density difference Delta Rho '' to produce said velocitydifference representation Vs in accordance with the expression: 17.Apparatus as in claim 16 wherein said representation Vs is combined withsaid flowrate measurement QT and said water phase proportion measurementYw to produce a representation of the flowrate Qw of said water phase inaccordance with the expression: Qw YwQT - Yw(1-Yw)A Vs (Qo (1-Yw)QT -Yw(1-Yw)A Vs) where A is the internal area of the cross section ofconduit through which said water-oil flow passes, whereby the flowrateof said oil phase is represented by the difference between the measuredtotal flowrate QT and the produced flowrate Qw.
 18. Apparatus forprocessing well logging data, comprising: means for deriving ameasurement representative of the proportion of one Phase of a multiplephase flow in a well at a selected depth level; and means for utilizingsaid derived measurement in conjunction with a predetermined value ofthe apparent difference in density between two phases of said flow toproduce a representation of the difference in velocity between said twophases of said multiple phase flow at said selected depth level in awell.
 19. Apparatus as in claim 18 wherein two phases are water and oiland said phase proportion measurement is the proportion of water in saidtwo phase flow.
 20. Apparatus as in claim 19 wherein said waterproportion measurement is Yw is combined with said value of apparentdensity difference Delta Rho '' to produce said velocity of differencerepresentation Vs in accordance with the expression: